Remove stems from tarragon. Peel the eggs, chop finely. Chop green onions and tarragon leaves. Mix eggs with herbs and mayonnaise, salt and pepper to taste.
Cut off the crusts from the bread, grease one side of each piece with a very thin layer of butter. Heat up a frying pan, put the pieces of bread butter side down and fry over medium heat until golden brown on one side only.
Transfer the bread to a board with the fried side down, spread the egg mixture into 2 pieces, cover with the remaining pieces of bread and press down. Cut the pieces diagonally in half and serve immediately.